One CNBC moderator questioned Graham about his notably centrist positions on some issues, including climate change and immigration.

Graham is the only GOP candidate who supports a comprehensive overhaul of the nation's current immigration laws that includes a path to citizenship for immigrants living in the country illegally.

And he has said the federal government should take steps to address climate change.

"I think I'm trying to solve problems that somebody better solve. Now you don't have to believe that climate change is real. I have been to the Antarctic. I have been to Alaska. I am not a scientist and I have the grades to prove it," he quipped.

He said: "But I have talked to the climatologists of the world and 90% of them are telling me that greenhouse-gas effect is real. That we're heating up the planet."

Graham, then shifting to a more exasperated tone, lamented about the party's losses in the last two presidential elections and ranted on the Democratic Party's top candidates, former US Secretary of State Hillary Clinton and Sen. Bernie Sanders (I-Vermont).

"At the end of the day, folks, I am trying to solve a problem and win an election! I am tired of losing! Good God, look at who we're running against!" he said, proceeding to refer, respectively, to Clinton and Sanders.

He said: "The No. 1 candidate on the other side thought she was flat broke after her and her husband were in the White House for eight years. The No. 2 guy went to the Soviet Union on his honeymoon and I don't think he ever came back! If we don't beat these people, who the hell are we going to beat?"

Graham earned props from 2012 Republican nominee Mitt Romney, who said it was clear he belongs on the main stage: